Solid state 12th Maharashtra state board

SOLID
STATE
12th HSC
PRESENTE
D BY:
FREYA
CARDOZO
PRESENTED BY: FREYA CARDOZO

What are solids?
Crystalline and Amorphous solids
Types of solids
• Ionic solids
• Molecular solids
• Covalent
• Metallic solid
Crystal lattic and
Types of Bravais Lattice

Classification of Solids
Crystalline Solids Amorphous Solids
 Regularity and periodicity in
arrangement of constituent particles in
solid
 Long range order
 All are anisotropic except cubic crystal
structure
 Have sharp M.P and B.P
 Eg. KCl, NaCl, Diamond etc
 Random arrangement of constituent
particles in solid
 Short range order
 All are isotropic in nature
 They boil or melt over a range of
temperatures
 Eg. Graphite, Glass, Sand etc

What is Anisotropy?
 Anisotropy is the property of a material
which allows it to change or assume different
properties when measured in different
directions.
 It can be defined as a difference, when
measured along different axes, in a
material's physical or mechanical properties
like absorbance, refractive
index, conductivity, tensile strength, etc

What is Isotropy?
 The phenomenon in which the physical
property of a solid does not change when
measured in any direction is called
isotropy
 Due to the random distribution of
amorphous solid they show this
property

Which is a crystalline and which is amporhous?
A B

Questions
 Distinguish between crystalline and amorphous solids
 Define anisotropy and isotropy

Isomorphism
 Same crystal structure
 Two or more substances the chemical
Composition has the same atomic ratio.
 For example (i) NaF and MgO (ii) NaNO3
and CaCO3 are isomorphous pairs, and have
the same atomic ratios, 1:1 and 1:1:3,
respectively, of the constituent atoms.

Polymorphism
• A single substance that exists in two or more forms or
crystalline
structures is said to be polymorphous.
• formed under different conditions.
• For example : Calcite and aragonite calcium carbonate;
α-quartz, b-quartz and cristobalite- Silica
• Polymorphism
occuring in elements is called allotropy. For
example: three polymorphic (allotropic) forms
of carbon are diamond, graphite and fullerene.

Types of Solids
 Ionic
 Covalent
 Molecular
 Metallic
1 2
3 4
Points to differentiation :-
Particles in each,
Type of interaction,
Conductance, Hard/Brittle,
Examples

Questions
 Solid that have same chemical ratio of atoms and same crystal structure are?
 Give one eg of polymorphism seen in elements
 Molecular solids are
a. crystalline solids
b. amorphous solids
c. ionic solids
d. metallic solids
 What are the types of particles in each of the four main classes of crystalline
solids ?
 Distinguish between ionic solids and molecular solids.

Definitions
 Lattice is a geometrical arrangement of points in a three
dimensional periodic array
 Basis are any atoms or ions that are placed on lattice
points
 A crystal structure is obtained by attaching a constituent
particle
to each of the lattice points. Such constituent particles that
are attached to the lattice points form the basis of the
crystal lattice or space lattice
 The smallest repeating structural unit of a crystalline solid
is called unit cell.
+

7 major types of crystals
1. Cu Cubic 3 Scc, Bcc, Fcc
2. Te Tetragonal. 2 Scc, Bcc
3. O Orthorhombic 4 Scc, Bcc, Fcc, Base.C.
4. Mo Monoclinic 2 * Scc, Base.C.
5. T Triclinic. 1 Scc
6. He Hexagonal 1 Scc
7. R Rhombic 1 Scc
Simple/Primitive -
Scc
Body centered -
Bcc
Face centered - Fcc
Base centered* -
Base.C.
CuTe Our MoTHeR

Crytal Systems

Types of unit cells
Types of unit cell : There are four types of unit cells.
Primitive or simple unit cell : In primitive unit cell, the constituent
particles are present at
its corners only.
 Body-centred unit cell : In this type of unit cell, one constituent
particle is present at
the centre of its body in addition to the corner particles.
 Face-centred unit cell : This unit cell consists of particles at the
centre of each of the faces in addition to the corner particles.
Base-centred unit cell : This unit cell
consists of particles at the centre of any two
of its opposite faces in addition to the corner
particles.
PRESENTED BY: FREYA CARDOZO Base Centered

Number of atoms per unit cell
How many of
these in a
cube??
Corners=
Faces=

SCC

Bcc
 At corners and in the body there are atoms
 corners contri 1/8
No of corner=8
Thus 1/8*8 = 1 atom utilized at corners
1 placed in the body
Thus total is 1+1=2 atoms

FCC
Corners= 8
But 1 atom at one corner is shared by 8
Thus contri of one is 1/8
Thus no of atoms at each corners is
1/8*8=1
No of faces= 6
1 atom shared by 2 i.e at one face there is
½ atom
So at 6 faces
6*1/2=3
Total atoms= 1+3 = 4 ..in fcc

Chalo ab tum batao
FCC mai kitna??
SCC mai kitna??
Bccc mai kitna??

OVERVIEW
Scc Bcc Fcc
Simple cubic
Atoms at corners oly
Body centered
Atoms at corner+ body
Face centered
Atoms at corners plus faces
1 atom/particle 1c+1b=2 1c+3f=4

Questions
 Calculate the number of atoms in fcc unit cell.
 Cesium chloride crystallizes in cubic unit cell with Cl ions at the
corners and a Cs⊕ ion in the centre of the cube. How many CsCl
molecules are there in the unit cell?
 2 A compound made of elements C and D crystallizes in fcc
structure. Atoms of C are present at the corners of the cube. Atoms
of D are at the centres of faces of the cube. What is the formula of
the compound?

Answers
 C – corners = 8 corners x 1/8 is contribution of each = 1 atom
 D – center of faces = 6 face x ½ contribution of each = 3 atom
 Thus, C1D3 is the formula of the crystal.

• Packaging of solids
• Derivation to calculate Density
• Calculating No.of particles, unit cells And No.of
unit cells in a given Volume
• Type 1 numericals

Derivation

Formula :- d= nM/a3 NA

Type 2 numericals
When gold crystallizes, it
forms face-centred cubic cells. The unit cell
edge length is 408 pm. Calculate the density
of gold. Molar mass of gold is 197 g/mol.

 An element with molar mass 27 g/mol forms cubic
unit cell with edge length of 405 pm. If density of the
element is 2.7g/cm3.What is the nature of cubic unit
cell?

Relationships

An element has a bcc structure with unit cell edge
length of 288 pm.Density of the element is 7.2
g/cm3. How many unit cells and number of atoms
are present in 200 g of the element?

Niobium forms bcc structure. The density of niobium
is 8.55 g/cm3 and length of unit cell edge is 330.6 pm.
How many atoms and unit cells are present in 0.5 g of
niobium

Packing of particles in crystal lattice
 Particles of a crystalline solid are close packed.
 During packing all atoms are considered as hard spheres
 Closer the packaging stronger the interparticle force of attraction. More
strong and stable the crystal is.
 Coordination number -The number of neighbouring spheres that touch any
given sphere is its coordination number
 Larger the magnitude of C.N more closely packed atoms, more compact is
the crystal.

Packaging
 1D packing – linear arrangment of
spheres
 2D packing can be done in 2 ways
1. square
2. Hexagonal
 placing layer two exactly over Layer 1 –
both layers same i.e AA type
 placing layer two in between the voids
of layer 1- different layers i.e AB type
Calculate coordination numbers!!
1D
AA Type
AB type

 3D packaging - Stacking of two dimensional layers gives rise
to three dimensional crystal structures.
 Two dimensional square close packed layers are found to
stack only in one way to give simple cubic lattice.
 Hexagonal close pack can be found in 2 types
 ABAB i.e HCP
 ABCABC i.e ccp

Simple cubic or primitive Cubic unit cell
(SC) Eg. Polonium
Each sphere is surrounded by
6 neighbouring spheres, 4 in its own
layer, 1 above and 1 below. Hence
coordination
number of any sphere in sc is 6.

Placing 3rd layer on hexagonal close pack

Voids
Tetrahedral Voids
Coordination
number = 4

Octahedral voids
Coordination
number=6

VOIDS
Number of voids per atom in hcp and ccp : The tetrahedral and octahedral
voids occur in hcp and ccp/fcc structures.
There are two tetrahedral voids associated with each atom.
The number of octahedral voids is half that of tetrahedral voids.
Thus, there is one octahedral void per atom.
If N denotes number of particles, then number of tetrahedral voids is
2N and that of octahedral voids is N.

ABAB type –hcp Mg, Zn

Ccp/fcc- ABCABC type
Eg.Cu and Ag

hcp and ccp/fcc structures that result
from stacking of hexagonal close packed
layers in two different ways, each sphere is
surrounded by 12 neighbouring spheres, 6 in
its own layer, 3 above and 3 below. Hence, the
coordination number of any sphere in hcp or
ccp/fcc structure is 12.

Questions
vi. Which of the following is not
correct?
a.Four spheres are involved in the
formation of tetrahedral void.
b. The centres of spheres in octahedral
voids are at the apices of a regulaR
Tetrahedron.
c.If the number of atoms is N the
Number of octahedral voids is 2N.
d. If the number of atoms is N/2, the
Number of tetrahedral voids is N.
vii. A compound forms hcp
structure.
Number of octahedral and
tetrhedral
voids in 0.5 mole of substance is
respectively
a. 3.011×1023, 6.022×1023
b. 6.022×1023, 3.011×1023
c. 4.011×1023, 2.011×1023
d. 6.011×1023, 12.022×1023

Type 1 Numericals
 A compound made of elements C and D crystallizes in fcc
structure. Atoms of C are present at the corners of the cube.
Atoms of D are at the centres of faces of the cube. What is the
formula of the compound?
 A compound is formed by two elements A and B.The atoms of
element B forms ccp structure. The atoms of A occupy 1/3rd of
tetrahedral voids. What is the formula of the compound ?
 In an ionic crystalline solid atoms of element Y form hcp lattice.
The atoms of element X occupy one third of tetrahedral voids.
What is the formula of the compound ?

A compound forms hcp structure. What is the
number of (a)
octahedral voids (b) tetrahedral voids (c) total
voids formed in 0.4 mol of it.

Recap: Stochiometric Defects
1. Vacancy defects
2. Self Interstitial impurity D.
3. Schottky D.
4. Frenkel D.

disorders or irregularities in the stacking of atoms.
Such irregularities in the arrangement of constituent particles of a
solid crystal are called defects or imperfections.
Why do these detects occur?
Due to improper crystallization – Faster process or impurities
present
Majorly 3 types
• point
• Line
• Plain

Point DeFects -These defects are
irregularities produced in the arrangement of
basis at lattice points in crystalline solids.
 Stoichiometric point defect
 Impurity defect
 Non-stoichiometric point defect

Stoichiometric defect
 What is stiochiometry
Chemical formula of a compound shows fixed ratio of number of atoms or
number of cations and anions. This fixed ratio is the stoichiometry of the
compound.
 Stiochometry unchanged. I.e same no of cation or anion or atoms as per
mol.formula
 Types
1. Vacancy defect
2. Self interstitial defect in elemental solid
3. Schottkydefect
4. Frenkel defect

Vacancy defect. Self interstitia D.
 particle is missing from its regular site in the
crystal lattice. The missing particle creates a
vacancy in the lattice structure
 vacancy defect be developed during
crystallization or when the substance is heated.
 Since particle is missing, mass decreases
 Volume unchanged
 Density decreases
 When some particles of a crystalline elemental solid occupy
interstitial sites in the crystal structure, it is called self
interstitial defect.
 This happens in 2 ways
1. An extra atom sits in interstitial space. Remaining atoms r
in their own space. Since, 1 extra particle
2. Mass increases and Density increases
3. One of the atom from the crystal leaves its own position
and occupies interstitial space. Since no atom is lost or
gained. Mass same this density unchanged

Schottky defect
 Its a type of bacany defect seen in an ionic solid
 A cation and anion are missing from their regular position. Loss of
either one leads to loss of the other also so that electrical neutrality is
maintained.
 Thus, there exist two holes per ion pair lost, one created by missing
cation and the other by a missing anion. Such a paired cation-anion
vacancy defect is a Schottky defect.
 Condition for formation
1. High degree of ionic character
2. High coordination number of anion
3. small diff in size of Cation n anion

 Consequence
1. since ions are missing mass decreases thus density decreases
2. Electrical neutrality maintained
Eg. NaCl, AgBr and KCl.

Frenkel defect
 Frenkel defect arises when an ion of an ionic
compound is missing from its regular lattice site
and occupies interstitial position between lattice
points.
 Cations are usually smaller than anions. It is,
therfore, more common to find the cations
occupying interstitial sites.
 Smaller cation is displaced from its normal site
to an interstitial space. It, therefore, creates a
vacancy defect at its original position and
interstitial defect at its new location in the same
crystal.
 Frenkel defect can be regarded
as the combination of vacancy defect and
interstitial defect.

 Conditions
1. Ions having low coordination numbers
2. Large difference in sizes of cation n anions
 consequences
1. As no ions are missing from the crystal lattice as a whole, the
density of solid and its chemical properties remain unchanged.
2. Electrical neutrality maintained
 Eg.. ZnS, AgCl, AgBr, AgI, CaF2

Impurity defect
 Impurity defect arises when foreign atoms, that is, atoms different
from the host atoms, are present in the crystal lattice.
 They are of two types
1. Substitutional impurity defect
 Solid solutions of metals (alloys)
 Vacancy through aliovalent impuriy
2. Interstitialal impurity defect

Substitution impuriy defects
 In this defect, the foreign atoms are found at the lattice sites in place of host atoms.
 The regular atoms are displaced from their lattice sites by impurity atoms.
Solid solution of Metal (alloy)
Eg. Brass( made of Cu with impurity of Zn)
Vacancy through Aliovalent impurity
Vacancies are created by the addition
of impurities of aliovalent ions (that is, ions
with oxidation state (o.s.) different from
that of host ions) to an ionic solid.
Impurity of SrCl2 in
NaCl…Sr2⊕ ions
Occupy some of the regular
sites of Na⊕ host . To
maintain electrical neutrality,
Sr2⊕ ion removes two
Na⊕ions. One of the vacant
lattice sites created by
removal of two Na⊕ ions is
occupied by one
Sr2⊕ ion. The other site of
Na⊕ ion remains
vacant

Interstitial Impurity defect
In this defect, the impurity atoms
occupy interstitial spaces of lattice
structure. For example in steel, Fe
atoms occupy normal lattice sites.
The carbon atoms are present at
interstitial spaces,

Nonstoichiometric defects
 Stochiometry is disturbed
 stoichiometry does not cause any change in the crystal structure.
 Nonstoichiometric defect arises when the ratio of number of atoms of one kind
to that of other kind or the ratio of number of cations to anions becomes
different from that indicated by its chemical formula
 Two types
1. Metal deficiency defect Eg. NiO and Ni0.97O1.0
2. Metal excess defect
 A neutral atom or an extra positive ion occupies interstitial position –ZnO and
Zn1+xO1.0
 By anion vacancies (Colour or F-centres) – NaCl and Na1+xCl1.0

Metal deficiency defect
 In compounds with variable oxidation states
 The cation from such compounds is missing
 The excess negative charge created due to
this is balanced by presence of cation of the
same metal with higher oxidation state than
that of missing cation.
 Eg. NiO, Ni2+ and O-2
 One Ni2+ is missing the excess charge is
balanced
By two Ni3+ atoms.
Stochiometry actually is Ni0.97O1.0

Metal excess defect: A neutral atom or an extra positive ion occupies
interstitial position
Thus the
Non-
stoichiometri
c formula is
Zn1+xO1.0

Metal excess defect:By anion vacancies (Colour or F-centres)
 This type of non stoichiometric defect imparts colour to
solid
 Eg. When NaCl is heated in atmosphere of Na, the Cl ions
from the crystal come to the surface and react with the Na
to form NaCl at the surface.
 the reaction with Na at the surface releases an electron
that occupies
The vacant spaces created by the Cl ions.
 The anion vacant sites occupied by electrons are
F-centres or colour center
 crystal this has extra Na atom
 Formula- Na1+xCl1.0

13. Explain with diagram, Frenkel defect. What are the conditions for its formation? What is its effect on
density
and electrical neutrality of the crystal?
14. What is an impurity defect? What are its types? Explain the formation of vacancies through aliovalent
impurity lwith example.
What are the consequences of Schottky defect?
iii. In Frenkel defect
a. electrical neutrality of the
substance is changed.
b. density of the substance is
changed.
c. both cation and anion are missing
d. overall electical neutrality is
preserved.

Electrical properties of solids
 CONDUCTORS
1. Solids having electrical conductivities in the range 104 to 107 Ohm-1m-1are called
conductors.
2. Metals and electrolytes (ionic solids) are examples of electrical conductors.
3. Metals conduct electricity by movement of electrons while electrolytes conduct
electricity by movement of ions.
 INSULATORS
1. Solids having low electrical conductivities in the range 10-20 to 10-10 Ohm-1m-1 are called
insulators.
2. Most nonmetals and molecular solids belong to this category.
 SEMICONDUCTORS
1. Solids having electrical conductivities in the range 10-6 to 104 Ohm-1 m-1 are
semiconductors.
2. This range is intermediate between conductors and insulators.
3. Metalloids like silicon, germanium belong to this category.

Used to explain the classification of substances
as metals, non metals and metalloid

Band theory
 A band is made of closely spaced electronic energy levels.
 Band formation can be correlated to formation of molecular orbitals
(MOs) by interaction of atomic orbitals
 According to MO theory interaction of atomic orbitals of combining
atoms results in formation of equal number of MOs which spread over the
entire molecule.
 Similar to this, interaction of energy levels of electrons in the closely
spaced constituent atoms in solids result in formation of bands.

Types of band
1. Conduction band
 The highest energy band containing electrons is the conduction band.
 It is formed by interaction of the outermost energy levels of closely spaced
atoms in solids.
 Conduction band may be partially occupied or vacant.
 Electrons in conduction band are mobile and delocalized over the entire
solid
 They conduct electricity when potential is applied

Valence band
 The band having lower energy than conduction band is the valence band.
 The electrons in valence band are not free to move because they are tightly
bound to the respective nuclei.

Band gap
 The energy difference between valence band and conduction band is
called band gap.
 Size of the band gap decides whether electrons from valence band can be
promoted to vacant conduction band or not
 when band gap is too large to promote electrons from valence band to
vacant conduction band by thermal energy, it is called forbidden zone.
 When band gap is small, electrons from higher energy levels in valence
band can be promoted to conduction band by absorption of energy (such
as thermal, electromagnetic).

Insulators
 Valence band is completely filled with electrons
and the conducation band is empty
 Both bands are seperated by separated a large
energy gap called forbidden zone
 Thermal energy is insufficient to promote
electrons

Conductors
 Outermost electrons of all the atoms in the metallic
crystal occupy conduction band.
 The number of electrons in conduction band of metals
is large. Hence metals are good conductors of
electricity
 Depending on which orbitals are involved in the
formation of band they are labbeled as s band p band
 Band formation in metallic conductors, thus, results in
delocalization of the outermost electrons of all the
metal atoms leaving behind metal ions.
 This is described as 'cations of metal are immersed in
the sea of electrons'.

 Give reason : conductivity of metals decreases with
increase in temperature
Metal cations occupying lattice positions in the
crystal are always in vibrational motion
When thermal energy is applied the vibrational
motion increases greatly due to which the Flow of
electrons is interrupted
Thus,…

Semiconductor
 Intermediate between CONDUCTORS and insulators
 The valence band in semiconductor is completely filled
with Electrons and conduction band is empty. However,
the energy gap between the two bands is smaller than that
in an insulator.
 At a temperature above absolute zero a few electrons in
the valence band have enough thermal energy to jump
through the small band gap and occupy higher energy
conduction band.
 The conduction band, thus, becomes partially filled and
the valence band becomes partially empty.
 Thus when potential is applied more es are promoted to
the conduction band
 Eg. Si and Ge

Intrinsic Semiconductors
At a temperature above absolute zero a
few electrons in the valence band have enough
thermal energy to jump through the small band
gap and occupy higher energy conduction
band. The conduction band, thus, becomes
partially filled and the valence band becomes
partially empty.

Extrinsic Semiconductors
 The conductance of an extrinsic Semiconductor can be increased by
adding minute small amount of impurities by a process called doping
 the added impuriy is called a dopant
 A doped semiconductor, having higher conductivity than pure intrinsic
semiconductor, is an extrinsic semiconductor
 These are of 2 types
1. n type
2. p type

Extrinsic conductors
n type p type
 Doped with grp 15 elements
 Charge carriers are electrons
 Eg. Si doped with P
 Extra electron from P, this helps increase
electrons in conduction band
 Contain More number of valence electrons that
of the pure semiconductor.
 Dopped with grp 13 elements
 Charge carriers are holes which behave as positive
charge
 Si doped with B
 One electron less than what is required to bond with Si
 Contain less number of valence electrons than that of
the pure semiconductor.

P type
 Impurity from group 13
 Boron atom has only three valence electrons. It does not have enough
electrons to form bonds with its four Si neighbours.B atom forms bonds
with three Si atoms only. The missing fourth electron creates an electron
vacancy. It is called a hole.
 A hole has a tendency to accept electron from its close vicinity. Thus, a
hole behaves as if it has a positive charge.
 The electrons in partially filled valence band move under the influence of
an applied potential. Theholes move in the opposite direction
 Because the charge carriers are holes which behave like positive charge,
the Si or Ge doped with group 13 element semiconductoor In, is a p-type
semiconductor.

N type
 Si has a crystal structure in which each Si atom is
linked tetrahedrally to four other Si atoms
 When P is added it occupies places in the lattice
 Four of the five valence electrons of P are utilized
in bonding the closest to four Si atoms. Thus, P
has one extra electron than needed for Bonding
 Because the charge carriers are the increased
number of electrons, Si or Ge doped with group
15 elements such as P, As, Sb or Bi is an n-type
semiconductor.

Question
ii. Which of the follwong is n-type
semiconductor?
a. Pure Si
b. Si doped with As
c. Si doped with Ga
d. Ge doped with In

Magnetic properties of solids
 Electrons spin about their own axis due to which a magnetic field is
induced
 Thus electrins act as tiny magnets
 If electrons are unpaired i.e single e in an orbital it will contribute to
magnetic field
 But paired es cancel each other’s spin this no magnetic field is generated
 3 types of magnetism
1. Diamagnetic
2. Paramagnetic
3. Ferromagnetic

Dimagnetic
 All electrons paired
 Electrons weakly replled by magnetic fields
 Pairing of electrons balances the spins and hence, cancels their magnetic
moments.
 N2, F2 ,NaCl, H2O and benzene are some examples of diamagnetic
substances.

Paramagnetic
 The substances with unpaired electrons
 Weakly attracted by Magnetic field
 The spinning of unpaired electron gives rise to a magnetic moment. The
substance is attracted by magnetic field because of magnetic moment.
 These substances exhibit magnetism in Presence of external magnetic
field only. They Lose magnetism when the external magnetic field is
removed.
 Oxygen, Cu2⊕, Fe3⊕, Cr3⊕ are some examples of paramagnetic substances.

Ferromagnetic
 large number of unpaired electrons
 attracted strongly by magnetic field
 These substances can be permanently magnetised.
They retain magnetism even after the removal of
external magnetic field.
 Some example of ferromagnetic substances are Fe,
Co, Ni, Gd, CrO2

Packaging efficiency like Coordination number indicates the Measure of
how tightly solids are packaged

Packaging efficiency calculation
 Formula

Scc(simple cubic)n=1
a = 2r or r = a/2

Bcc (Body Centered cubic) n=2
FED and AFD

FCC(Face centered cubic) n=4
The triangle ABC is right angled
with ∠ABC = 90
AC

 coordination number

Same as ccp and hcp

vii. Pb has fcc structure with edge length
of unit cell 495 pm. Radius of Pb
atom is
a. 205 pm b. 185 pm
c. 260 pm d. 175 pm
 Cu crystallizes in Bcc unit cell with edge length of 495 pm. What
is the
radius of Cu atom?

The unit cell of metallic silver is fcc. If radius of Ag atom is 144.4
pm, calculat
(a) edge length of unit cell
(b) volume of Ag atom,
(c) the percent of the volume of a unit cell, that is occupied by Ag
atoms,
(d) the percent of empty space.

4. The density of iridium is 22.4 g/cm3. The unit cell of iridium is fcc.
Calculate the radius of iridium atom. Molar mass of iridium is 192.2 g/mol.
5. Aluminium crystallizes in cubic close packed structure with unit cell edge
length of 353.6 pm. What is the radius of Al atom? How many unit cells are
there in 1.00 cm3of Al? (125 pm, 2.26×1022)

Solid state 12th Maharashtra state board

Recomendados

Recomendados

Mais conteúdo relacionado

Mais procurados

Mais procurados (20)

Semelhante a Solid state 12th Maharashtra state board

Semelhante a Solid state 12th Maharashtra state board (20)

Mais de Freya Cardozo

Mais de Freya Cardozo (20)

Último

Último (20)

Solid state 12th Maharashtra state board